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Simplifying 4x2 + -48x + 5 = 0 Reorder the terms: 5 + -48x + 4x2 = 0 Solving 5 + -48x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -12x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -12x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -12x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -12x + x2 = 0 + -1.25 -12x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -12x + x2 = -1.25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -1.25 + 36 Reorder the terms: 36 + -12x + x2 = -1.25 + 36 Combine like terms: -1.25 + 36 = 34.75 36 + -12x + x2 = 34.75 Factor a perfect square on the left side: (x + -6)(x + -6) = 34.75 Calculate the square root of the right side: 5.894913061 Break this problem into two subproblems by setting (x + -6) equal to 5.894913061 and -5.894913061.Subproblem 1
x + -6 = 5.894913061 Simplifying x + -6 = 5.894913061 Reorder the terms: -6 + x = 5.894913061 Solving -6 + x = 5.894913061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.894913061 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.894913061 + 6 x = 5.894913061 + 6 Combine like terms: 5.894913061 + 6 = 11.894913061 x = 11.894913061 Simplifying x = 11.894913061Subproblem 2
x + -6 = -5.894913061 Simplifying x + -6 = -5.894913061 Reorder the terms: -6 + x = -5.894913061 Solving -6 + x = -5.894913061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.894913061 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.894913061 + 6 x = -5.894913061 + 6 Combine like terms: -5.894913061 + 6 = 0.105086939 x = 0.105086939 Simplifying x = 0.105086939Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.894913061, 0.105086939}
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